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Of the science books in a certain supply room, 50 are on

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Of the science books in a certain supply room, 50 are on [#permalink]

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New post 21 Apr 2012, 21:17
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Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?

A. 81
B. 159
C. 166
D. 285
E. 324
[Reveal] Spoiler: OA

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Of the science books in a certain supply room, 50 are on [#permalink]

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New post 21 Apr 2012, 22:11
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boomtangboy wrote:
16. Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?

(A) 81
(B) 159
(C) 166
(D) 285
(E) 324


We can remove 80 books only from physics or from chemistry. Worst case scenario would be if we remove all books on botany, zoology, geology, 79 books on physics and 79 books on chemistry.

We would have 50(botany) + 65(zoology) + 50(geology) + 79(physics) + 79(chemistry) = 323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either on physics or on chemistry.

Answer: E.

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Re: Of the science books in a certain supply room, 50 are on [#permalink]

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New post 22 Apr 2012, 01:15
Thanks Bunel. Very helpful response yet again!

Is this the only way to solve this?
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Re: Of the science books in a certain supply room, 50 are on [#permalink]

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Re: Of the science books in a certain supply room, 50 are on [#permalink]

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New post 04 Sep 2014, 17:29
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Re: Of the science books in a certain supply room, 50 are on [#permalink]

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boomtangboy wrote:
Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?

A. 81
B. 159
C. 166
D. 285
E. 324


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Of the science books in a certain supply room, 50 are on [#permalink]

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New post 17 Dec 2015, 08:22
Bunuel wrote:
boomtangboy wrote:
16. Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?

(A) 81
(B) 159
(C) 166
(D) 285
(E) 324


We can remove 80 books only from physics or from chemistry. Worst case scenario would be if we remove all books on botany, zoology, geology, 79 books on physics and 79 books on chemistry.

We would have 50(botany) + 65(zoology) + 50(geology) + 79(physics) + 79(chemistry) = 323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either on physics or on chemistry.

Answer: E.

Similar questions to practice:
12-easy-pieces-or-not-126366.html#p1033935
in-his-pocket-a-boy-has-3-red-marbles-4-blue-marbles-and-85216.html
of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html
in-a-deck-of-52-cards-each-card-is-one-of-4-different-color-83183.html
a-box-contains-10-red-pills-5-blue-pills-12-yellow-56779.html
each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html
a-student-is-asked-to-pick-marbles-from-a-bag-that-contains-72390.html

Hope it helps.


Bunuel, you used the URL to the solution of the problem listed here: 12-easy-pieces-or-not-126366.html#p1033935 rather than to the problem itself.
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Of the science books in a certain supply room, 50 are on [#permalink]

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New post 03 Jan 2016, 12:44
What is the number at which picking one more book will guarantee that a thresold of 80 has been surpassed in one science?

Imagine you are playing a rigged game. The object of the game is for you to draw 80 books from the same science. The person attempting to cheat you out of winning picks out the books for you. He or she tries to prevent you from drawing the winning number of books until it is no longer possible to do so. He or she first starts off by picking books that cannot reach the 80 threshold and does so until such books are exhausted. He or she then starts picking books out of one the two remaining sciences until he reaches 79. To delay reaching the 80 thresold as much as possible he or she then shifts to the last science until he or she reaches 79. At this point it is no longer possible to cheat you out of winning and when the next book is drawn, you meet the 80 book threshold. The number of books drawn at that point is therefore 50 + 65 + 50 + 79 + 79 + 1 = 324.
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Re: Of the science books in a certain supply room, 50 are on [#permalink]

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New post 09 May 2016, 16:02
I had a different approach.

You know that only books you can remove to get 80 of the same science is Physics (90) or Chemistry (110). Probability of drawing out a Chemistry is higher with every draw 110/365 vs 80/365. Logically you'll need to take out fewer books to 80 of the Chemistry. So you look at Physics books instead. Because the question says 'ensure'.

P(Physics) = 90/365 simplify to 90/360 or 1/4. You know that for every 4 books you take out 1 is likely to be a physics book. Then to get 80 physics books you need to take out 80 x 4 = 320. Answer is (E)
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Re: Of the science books in a certain supply room, 50 are on [#permalink]

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New post 11 May 2016, 20:31
[quote="Bunuel"]Bumping for review and further discussion*. Get a kudos point for an alternative solution!

Had an alternative approach

To ensure you get at least 80 books, you only look at Physics or Chemistry. 90 or 110. I calculated what percentage 80 books were of each group and took the highest percentage (i.e. 80/90 for Physics) and multiplied it by the total number of books (365). This makes sure you get 80 of one science as it makes sure you get 80 of the science that has the fewer books (i.e. harder probability). This gives you exactly 324.
Re: Of the science books in a certain supply room, 50 are on   [#permalink] 11 May 2016, 20:31
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